I know of a few of ways to express sharing in a pure language:
1) "Observable sharing", which, in general, is unsafe.
http://www.cs.chalmers.se/~koen/pubs/entry-asian99-lava.html
2) Using Template Haskell
http://www.dcs.gla.ac.uk/publications/PAPERS/7524/EmbedHDLinTH.ps
3) Matthew Naylor has done some work on "expressible sharing", which has
advantages over both methods above. I don't have any reference though...
4) Use a monad (but I'm sure this is what you're trying to avoid).
/ Emil
On 2008-02-08 07:33, Tom Hawkins wrote:
> I've been programming with Haskell for a few years and love it. One
> of my favorite applications of Haskell is using for domain specific
> languages. However, after designing a handful of DSLs, I continue to
> hit what appears to be a fundamental hurdle -- or at least I have yet
> to find an adequate solution.
>> My DSLs invariably define a datatype to capture expressions; something
> like this:
>> data Expression
> = Add Expression Expression
> | Sub Expression Expression
> | Variable String
> | Constant Int
> deriving Eq
>> Using the datatype Expression, it is easy to mass a collections of
> functions to help assemble complex expressions, which leads to very
> concise programs in the DSL.
>> The problem comes when I want to generate efficient code from an
> Expression (ie. to C or some other target language). The method I use
> invovles converting the tree of subexpressions into an acyclic graphic
> to eliminate common subexpressions. The nodes are then topologically
> ordered and assigned an instruction, or statement for each node. For
> example:
>> let a = Add (Constant 10) (Variable "i1")
> b = Sub (Variable "i2") (Constant 2)
> c = Add a b
>> would compile to a C program that may look like this:
>> a = 10 + i1;
> b = i2 - 2;
> c = a + b;
>> The process of converting an expression tree to a graph uses either Eq
> or Ord (either derived or a custom instance) to search and build a set
> of unique nodes to be ordered for execution. In this case "a", then
> "b", then "c". The problem is expressions often have shared,
> equivalent subnodes, which dramatically grows the size of the tree.
> For example:
>> let d = Add c c
> e = Add d d -- "e" now as 16 leaf nodes.
>> As these trees grow in size, the equality comparison in graph
> construction quickly becomes the bottleneck for DSL compilation.
> What's worse, the phase transition from tractable to intractable is
> very sharp. In one of my DSL programs, I made a seemingly small
> change, and compilation time went from milliseconds to
> not-in-a-million-years.
>> Prior to Haskell, I wrote a few DSLs in OCaml. I didn't have this
> problem in OCaml because each "let" expression was mutable, and I
> could use the physical equality operator to perform fast comparisons.
> Unfortunately, I have grown to love Haskell's type system and its lack
> of side effects, and could never go back.
>> Is there anything that can be done to dramatically speed up
> comparisons, or is there a better approach I can take to extract
> common subexpressions? I should point out I have an opportunity to
> get Haskell on a real industrial application. But if I can't solve
> this problem, I may have to resort to far less eloquent languages.
> :-(
>> Thanks for any and all help.
>> -Tom
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